## Modelling Meme Distribution Using Hybrid Systems

At the beginning of our class we discussed a very basic model of a social network: each node is a person and each edge is a connection between people. This is robust enough for basic things, such as the varieties of closure and connectiveness that we have been learning. However, it is a very static model – we cannot make robust guesses about what information is doing in the system. We can get a deeper understanding of information flow within a network by modeling it as a hybrid system. That is to say, “a feedback interconnection of a discrete-state stochastic process … with a family of continuous-state stochastic dynamical systems.” (1)

Simply put, this means that each node is not so much a single entity, in this example, a website, but rather a collection of smaller entities, the users of a website. Within these nodes there is a continuous process that models the distribution of certain qualities. Once the distribution reaches a maximum threshold, it jumps (the discrete process) to the next node. This is a common way of modelling things such as transference of diseases.

The authors took this idea of modelling transference of diseases and used it to model the transference of memes online. By using websites and their denizens as the “infected,” one can using different machine learning techniques to model how memes jump between websites and other users. Once solid, predictive models of the transference of memes were established, the authors continued to find which communities are good “sensors” of memes. Good sensors are websites that post early in the lifetime of a meme and the chance of them posting early is independent of their earliness in posting other memes.

We can see very clearly how a simple model, with certain expansions, can create a very useful tool for describing seemingly very complex interactions and systems.

References-

(1) “Toward Emerging Topic Detection for Business Intelligence: Predictive Analysis of `Meme’ Dynamics” *Kristin Glass, Richard Colbaugh*, 2010. arXiv